Simplify the following expression: $t = \dfrac{88r^3}{-66r^3 - 121r^2}$ You can assume $r \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $88r^3 = (2\cdot2\cdot2\cdot11 \cdot r \cdot r \cdot r)$ The denominator can be factored: $-66r^3 - 121r^2 = - (2\cdot3\cdot11 \cdot r \cdot r \cdot r) - (11\cdot11 \cdot r \cdot r)$ The greatest common factor of all the terms is $11r^2$ Factoring out $11r^2$ gives us: $t = \dfrac{(11r^2)(8r)}{(11r^2)(-6r - 11)}$ Dividing both the numerator and denominator by $11r^2$ gives: $t = \dfrac{8r}{-6r - 11}$